Comparative study of the phase diagrams of spin- 1/2 and spin-1 antiferromagnetic chains with dimerization and frustration

The ground-state 'phase' diagrams and some low-energy properties of isotropic antiferromagnetic spin- 1/2 and spin-1 chains with a next-nearest-neighbour exchange J2 and an alternation δ of the nearest-neighbour exchanges have been compared for the first time using the density matrix renormalization group method. In the spin- 1/2 chain, the system is gapless for δ = 0 and J2 2c = 0.241, and is gapped everywhere else in the J2-δ plane. At J2c, for small δ, the gap increases as δα, where α = 0.0667 ± 0.001. 2J2 + δ = 1 is a disorder line. To the left of this line, the structure factor S(q) peaks at qmax = π (the Neel 'phase'), while to the right, qmax decreases from π to π/2 (the spiral 'phase') as J2 increases. We also discover a '↑↑&darr&darr phase' for large values of both J2 and δ. In the spin-1 case, we find a line running from a gapless point at (J2, δ) = (0, 0.25 ± 0.01) up to a 'gapless' point at (0.73 ± 0.005, 0) such that the open-chain ground state is fourfold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin- 1/2 case, but the line ends at about δ = 0.136. Similarly to the spin- 1/2 case, to the left of this line, the peak in the structure factor is at π (the Neel 'phase'), while to the right of the line, it is at less than π (the spiral 'phase'). For δ = 1, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin- 1/2 and spin-1 ladders.